At each of the denoising timesteps \(t\) , EDGE predicts the denoised sample and noises it back to timestep \(t-1\)  : \(\mathbf {\hat{z}}_{t-1} \sim q(\mathbf {\hat{x}}_\theta (\mathbf {\hat{z}}_t, \mathbf {c}), t-1)\) , terminating when it reaches \(t=0\)  (fig:2, right).
We train our model using classifier-free guidance [1]}, which is commonly used in diffusion-based models [2]}, [3]}, [4]}, [5]}, [6]}.
Following Ho et al. [1]}, we implement classifier-free guidance by randomly replacing the conditioning with \(\mathbf {c} = \emptyset \)  during training with low probability (e.g. 25%).
Guided inference is then expressed as the weighted sum of unconditionally and conditionally generated samples:
\( {\mathbf {\tilde{x}}(\mathbf {\hat{z}}_t, \mathbf {c}) = w \cdot \mathbf {\hat{x}}(\mathbf {\hat{z}}_t, \mathbf {c}) + (1 - w) \cdot \mathbf {\hat{x}}(\mathbf {\hat{z}}_t, \emptyset ).}\) 
